Machine Learning Hand in Hand with Control Theory

Modern control systems increasingly rely on machine learning to operate in complex, uncertain, and high-dimensional environments. At the same time, control theory offers powerful tools for understanding and improving machine-learning algorithms themselves. This docent lecture explores my research topic at the intersection of these two complementary directions, emphasizing the central role of continuous-time models.

I will first provide a general introduction to scientific machine learning and its application in control, where continuous-time dynamical systems serve as a framework for identifying, analyzing, observing, and ultimately controlling real-world processes. I present how learning-based tools can enhance classical control methods, from learning Lyapunov functions for stability analysis to data-driven observer design and structure-aware system identification, which supports real-time, model-based control.

Briefly, I turn to control for machine learning, demonstrating how ideas from dynamical systems and feedback theory can inform the design of more effective training algorithms. Viewing optimization and learning procedures as controlled continuous-time flows reveals new ways to improve stability, robustness, convergence, and long-time behavior of modern machine-learning models.

Together, these two perspectives highlight a bidirectional exchange where learning enriches control and control, in turn, enriches learning. By integrating guarantees from control theory with the flexibility of machine learning, this research aims to build reliable, interpretable, and high-performance models for complex dynamical systems.